Differentiation Calculator

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Example

Created on 2024-06-20Asked by Layla Nelson (Solvelet student)

Find the derivative of the function

f(x) = x^3 + 2x^2 - 3x + 1

Solution

Step 1: Identify the function

f(x) = x^3 + 2x^2 - 3x + 1

. Step 2: Use the power rule for differentiation:

\frac{d}{dx} (ax^n) = nax^{n-1}.

Step 3: Apply the power rule to each term:

f'(x) = 3x^2 + 4x - 3.

Step 4: Conclusion. The derivative of

f(x) = x^3 + 2x^2 - 3x + 1

f'(x) = 3x^2 + 4x - 3

. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Jackson Moore on Solvelet

1. Find the derivative of the function

f(x) = 3x^2 - 2x + 1

.2. Determine the slope of the tangent line to the curve

y = \sqrt{4 - x^2}

at the point

(1, \sqrt{3})

DefinitionDifferentiation is a basic concept in calculus, which allows us to find the rate of change, i.e., the slope of the function at a certain point. Differentiation is a fundamental tool in calculus which can be used to analyze and model functions, determine relative and absolute extrema of functions, solve differential equations, and much more. The derivative of a function f(x) with respect to its independent variable x can be written as f′(x) = dfdx(x). For ex:, the derivatire of the function f(x)=x2 with respect to x is f′(x)=2x, the slope of the tangent to the curve y=x2 at any point x.Learn & solve Differentiation related problems with SolveletAI advanced step-by-step solutions.

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